A Complete Finite Axiomatisation of the Equational Theory of Common Meadows

被引：1

作者：

Bergstra, Jan A. ^{[1
]}

Tucker, John v ^{[2
]}

机构：

[1] Univ Amsterdam, Informat Inst, Amsterdam, Netherlands

[2] Swansea Univ, Dept Comp Sci, Swansea, Wales

来源：

ACM TRANSACTIONS ON COMPUTATIONAL LOGIC | 2025年 / 26卷 / 01期

关键词：

arithmetical data type; division by zero; error value; common meadow; fracterm; fracterm calculus; equational theory; FRACTIONS;

D O I：

10.1145/3689211

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value perpendicular to whose main purpose is to always return a value for division. To rings and fields, we add a division operator x/y and study a class of algebras called common meadows wherein x/0 = perpendicular to. The set of equations true in all common meadows is named the equational theory of common meadows. We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable.

引用

页数：28